Pulsed NMR techniques are used in instruments for the measurement of the type, property and quantity of lattice bound and free, magnetically active nuclei within a sample. Some of the substances and properties that have been measured by NMR techniques are: moisture, polymers and copolymers, oils, fats and crystalline materials.
Pulsed NMR uses a burst or pulse of energy that is designed to excite the nuclei of a particular nuclear species of a sample being measured (the protons, or the like, of such sample having first been precessed in an essentially static magnetic field); in other words the precession is modified by the pulse. After the application of the pulse there occurs a free induction decay (FID) of the magnetization associated with the excited nuclei. That is, the transverse magnetization associated with the excited nuclei relaxes back to its equilibrium value of zero. This relaxation produces a changing magnetic field which is measured in adjacent pickup coils. A representation of this relaxation is the FID curve.
The analysis method described herein and in the above related patents and applications is to decompose the FID waveform into a group of separate time function equations. The coefficients of these equations are derived from the FID by use of a Marquardt-Levenberg (M-L) iterative approximation that minimizes the Chi-squared function--a technique well known in the art. Some of the time function equations found useful are: Gaussians, exponentials, Abragams, and trigonometric. From these time functions a set of parameters is calculated. Some of these parameters are ratios of the y-axis intercepts, squares and cross products of these ratios, and decay times for each of the time curves. In addition the sample temperature may form the basis for another parameter.
But, relating these parameters, quantitatively and qualitatively, back to the species of target nuclei is required. In the above referenced patent applications, the system is calibrated with known samples, and a `regression line` is generated which relates the parameters to the types, properties and quantities of the target nuclei. An unknown sample is introduced and the time functions are derived via the M-L iteration, and the parameters are calculated. The parameters are "regressed" via the "regression line" to yield the types, properties and quantities of target nuclei in the unknown sample. That is, the measured parameters from the unknown FID are used with the "regression line", and the types, properties and quantities in the unknown sample are determined. It is to be understood that the multidimensional "regression line" may not be graphically represented. As a simple regression technique example, consider that the grade point average of each of the students at a college were related to that student's SAT score and high school standing (forming a three dimensional space). The line formed is a "regression line" (which may be graphed). A new student's grade point average may be predicted by placing the student's SAT and high school standing on the "regression line,, and "reading" the grade point average.
It is a principal object of the present invention to relate the type, property and quantity of target nuclei of interest accurately and precisely.